Which square numbers added together make other square numbers?

Question

Excluding 9 & 16 and 144 & 256. Nothing to do with magic squares!

Answer 1

lets say those numbers are x and y and addition of their square is the square of another number z

so the equation becomes

x^2+y^2 = z^2

now put any value of x, y (except the numbers you have mentioned) and see whether the addition becomes a square

Now imagine the squares of natural numers and they are

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 etc.. and take this as value of z^2

Now assume natural numbers for x and calculate the square and they are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 etc..

now see whether the difference of z^ and x^2 becomes a square of a natural number (this has to be seen in corelation to all numbers to rest others)

from here we get, sets of three numbers where two adds up to equal to third are

9, 16, 25
25,144, 169
etc.. you really need to do a lot of trial and error here ... :)

Answer 2

You can construct an infinite number of such sets of square numbers, also known as "Pythagorean triples". The method has been known for a very long time. Here it is.

Pick any two numbers P and Q, one of them even and the other one odd. Calculate the numbers A = P^2 - Q^2, B = 2 * P * Q, and C = P^2 + Q^2. You will find that in every possible case, A^2 + B^2 = C^2.

If P and Q have a common factor, then so will A, B and C.

Example 1: P = 6, Q = 11, A = 85, B = 132, C = 157, no common factor.
Example 2: P = 6, Q = 15, A = 189, B = 180, C = 261, common factor 9.

Answer 3

This Site Might Help You.

RE:
Which square numbers added together make other square numbers?
Excluding 9 & 16 and 144 & 256. Nothing to do with magic squares!

Answer 4

Thinking about Pythagorian triples:

3, 4, 5 is an example: 3^2 + 4^2 = 5^2 (9 + 16 = 25)
There's also:

5, 12, 13: 5^2 + 12^2 = 13^2 (25 + 144 = 169)

I just noticed you didn't want 3, 4, 5 as an example.

How about 6, 8, 10, which is essentially double 3, 4, 5?
6^2 + 8^2 = 10^2 (36 + 64 = 100).

How about 9, 12, 15? 9^2 + 12^2 = 81 + 144 = 125.

Use any multiple of {3,4,5} and you'll get an infinite number of them.

Answer 5

MM's answer is a little misleading. You DO NOT have to import the Math package. It's part of lang and so it's always there. You need to define some variable before the loop: int cntSqrd = 0; int sum = 0; Then in the loop:, add these: cntSqrd = count*count; sum = sum + cntSqrd; // I'm assuming that you want the sum of the odds squared.

Answer 6

Any multiples of these sets will fulfill your requirements where sum of squares of first 2 numbers will be equal to square of 3rd number..........

(3,4,5) i.e. 9 and 16
(5,12,13) i.e. 25 and 144
(7,24,25) i.e. 49 and 576
(8,15,17) i.e 64 and 225..............etc